A rectangle has a length of 4 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. Graph a system of linear equations to find x.

Answer:

D

Step-by-step explanation:

Because their slopes are equal. Rest of the step-by-step explanation is in the attached file!!

Answer:

-5/4; -4/3

Step-by-step explanation:

12x^2 + 31x + 20 =

(4x + 5)(3x + 4) -->

x = -5/4 OR -4/3

Answer:

C

Step-by-step explanation:

A. 558 m2

B. 976 m2

C. 1,680 m2

D. 1,750 m2

Answer:

1064.64

Step-by-step explanation:

Answer:

335 = 50 + 6p

Step-by-step explanation:

50 +6p=335

subtract from both sides

-50      -50

6p=285

/6p   /6p

divide both sides

p=47.5

Answer:

15.50=25.25

Step-by-step explanation:

15+0.50=15.50

25+0.25=25.25

So 15+0.50=25.25 = 9.75 because you subract 25.25-15.50=9.75

Hope this helps

Answer:

4/5 (not drawing a black marble)

3/10 (drawing a red marble)

Step-by-step explanation:

Answer:

(A)One-third(36)(7)= 84 cubic units

Step-by-step explanation:

Volume of a Pyramid = [tex]\frac{1}{3}X$Base Area X Height[/tex]

The base is a rectangle

Base Area = 9 X 4=36 Square Units

Height =7 Units

Therefore:

Volume  [tex]=\frac{1}{3}(36)(7)[/tex]

=84 Cubic Units

Answer:

Step-by-step explanation:

Teh value of x is 23° (D)

Step-by-step explanation:

Total of angel = 360°

The value of x :

(2x + 15)° + 119° + 99° + 81° = 360°

2x + (15 + 119 + 99 + 81)° = 360°

2x + 314° = 360°

2x = 360° - 314°

2x = 46

x = 46 ÷ 2

x = 23°

So, the value of x is 23° (D)

Hope it helpful and useful :)

Answer:

Yes because 10 times 8 is 80.

Step-by-step explanation:

Answer: 80 IS a multiple of 10 because 8 times 10 is 80.

Step-by-step explanation:

Answer:6.3

Step-by-step explanation: 6.8 +1.5 -1.2 -0.8=6.3

The amount of flour left is 6.3 kg.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total flour = 6.8 + 1.5 = 8.3 kg

Amount of flour used = 1.2 + 0.8 = 2 kg

The amount of flour left.

= 8.3 - 2

= 6.3 kg

Thus,

6.3 kg of flour is left.

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Answer:

$19.99

Step-by-step explanation:

Take the price for 2 pairs and divide by 2 to get the price for one pair

39.98 /2

19.99 for one pair

Answer:

I mean I guess sure

Step-by-step explanation:

Anyway hope you have a good day!!

ig..

Answer:

40 miles

Step-by-step explanation:

Let's set x to the number of miles driven, and t to the number of hours it took to drive.

We know that 40t is equal to x.

We also know that 40t is equal to 30(t + 1/3).

Solve for t:

40t = 30(t+1/3)

40t = 30t + 10

Subtract 30t from both sides:

10t = 10

Divide 10 from both sides:

t = 1

40t = 40 x 1 = 40 miles

I drove 40 miles.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Suppose, I drove n number of miles and it took me x time in hours.

We know that 40x is equal to n.

Since it would take 20 more minutes, so we have the division of 20/60 = 1/3

Then, 40x is equal to 30(x+ 1/3).

Solve for t:

40x = 30(x+1/3)

40x = 30x + 10

10x = 10

Now , divide by 10 on both sides,

x = 1

40x = 40 x 1 = 40 miles

Therefore, I drove 40 miles.

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Answer: The new drawing would be larger than the first drawing.

Step-by-step explanation:

A scale factor greater that one is an enlargement, but one smaller than one is a reduction

The second drawing will be 5 times bigger than the first one.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

Given in the first drawing scale factor is 1:60

So Andre takes 60 units as 1

For example, it is 60 inches to 1 inch.

In the second drawing, Andre took 1:12

So he took 12 units as 1

For example 12 inches to 1

Now multiply by 5 then 5:60

So 60 inches to 5 inches means the second drawing is 5 times bigger the first one.

Hence "The second drawing will be 5 times bigger than the first one".

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ANSWER: The statistical procedure that should be performed is REGRESSION.

Step-by-step explanation: Regression is a statistical procedure that is used to estimate the relationship between an independent variable and a dependent variable using their mean values.

The independent variable in this case is the hours each student spend in studying, while the dependent variable is the students grade.

Since the researcher wants to determine if the hours a student spend in studying maths and science has any significant effect on their grades. The researcher should use regression, because it will show if the two variables are related and how it relates, by showing how far the points are from the trend lines of the graph.

Answer:

90

Step-by-step explanation:

2*30= 60

3*30= 90

Answer:

The answer is digit

Step-by-step explanation:

A single number between 0 and 9 is a digit, which often makes up larger numbers.

Final answer:

45 students need to make it to the boat to be rescued.

Explanation:

The question asks us to calculate how many students attended a field trip, given that 15% of the 300 students at a middle school attended.

Therefore, 45 students need to make it to the boat to be rescued.

Answer:

(a) Is not possible

(b) It is possible

(c) It is possible

(d) Is NOT possible.

Step-by-step explanation:

(a)

Is not possible, notice that for any function [tex]g[/tex]  such that

[tex]g : \mathbb{R} \rightarrow \mathbb{R}[/tex]

you would have that

[tex](g\circ f)(x) = g(f(x)) = g(|x|)[/tex]

And for, lets say -3,3 you have that

[tex]g(|-3|) = g(|3|) = g(3)[/tex] therefore is not possible to find a function that is one to one.

(b)

It is possible. Take the following function

[tex]g(x) = x\sin(x)[/tex] since [tex]\sin[/tex] is periodic it will take positive and negative numbers and if you multiply by [tex]x[/tex] each period will become bigger and bigger.

(c)

It is possible. Take the function

[tex]g(x) = \sqrt{x}[/tex]

Then

[tex](f \circ g )(x) = | \sqrt{x} | = \sqrt{x}[/tex]    and [tex]\sqrt{x}[/tex] is one to one.

(d)

It is NOT possible because   [tex](f\circ g)(x) = f(g(x)) = |g(x)|[/tex] and that will always be positive.  

Answer:

The number of candies in the sixth jar is 42.

Step-by-step explanation:

Assume that there are x number of candies in each of the six jars.

⇒ After Alice moves half of the candies from the first jar to the second jar, the number of candies in the second jar is:

[tex]\text{Number of candies in the 2nd jar}=x+\fracx}{2}=\frac{3}{2}x[/tex]

⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:

[tex]\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x[/tex]

⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:

[tex]\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x[/tex]

⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:

[tex]\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x[/tex]

⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:

[tex]\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x[/tex]

Now, it is provided that at the end, 30 candies are in the fourth jar.

Compute the value of x as follows:

[tex]\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}[/tex]

Compute the number of candies in the sixth jar as follows:

[tex]\text{Number of candies in the 6th jar}=\frac{63}{32}x\\[/tex]

                                                    [tex]=\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42[/tex]

Thus, the number of candies in the sixth jar is 42.

There are now 33.75  candies in the sixth jar.

Let's denote:

-  x  as the initial number of candies in each jar.

After Alice moves half of the candies from the first jar to the second jar, the number of candies in the first jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the second jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .

After Boris moves half of the candies from the second jar to the third jar, the number of candies in the second jar becomes [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the third jar becomes  [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .

After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the third jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the fourth jar becomes  [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .

After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fourth jar becomes  [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the fifth jar becomes [tex]\( \frac{3x}{4} + \frac{3x}{8} = \frac{9x}{8} \).[/tex]

Finally, after Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the fifth jar becomes [tex]\( \frac{9x}{16} \)[/tex], and the number of candies in the sixth jar becomes [tex]\( \frac{9x}{16} + \frac{9x}{32} = \frac{27x}{32} \).[/tex]

Given that 30 candies are now in the fourth jar, we can set up the equation:

[tex]\[ \frac{3x}{4} = 30 \][/tex]

Solving for  x :

[tex]\[ x = \frac{4 \times 30}{3} = 40 \][/tex]

Now, we can find the number of candies in the sixth jar:

[tex]\[ \frac{27 \times 40}{32} = \frac{1080}{32} = 33.75 \][/tex]

So, there are now 33.75  candies in the sixth jar.

Answer:

It will take 36.1 years for her money to reach $105,000.

Step-by-step explanation:

The amount of money earned after t years in continuous interest is given by:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.

This means that [tex]P(0) = 7000, r = 0.075[/tex]

How long will it take for her money to reach $105,000?

This is t for which P(t) = 105000.

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]105000 = 7000e^{0.075t}[/tex]

[tex]e^{0.075t} = \frac{105000}{7000}[/tex]

[tex]e^{0.075t} = 15[/tex]

[tex]\ln{e^{0.075t}} = \ln{15}[/tex]

[tex]0.075t = \ln{15}[/tex]

[tex]t = \frac{\ln{15}}{0.075}[/tex]

[tex]t = 36.1[/tex]

It will take 36.1 years for her money to reach $105,000.

Answer: The Sun is the major source of energy for organisms and the ecosystems of which they are a part. Producers such as plants, algae, and cyanobacteria use the energy from sunlight to make organic matter from carbon dioxide and water. This establishes the beginning of energy flow through almost all food webs.

Answer:

  0.56 mg

Step-by-step explanation:

Put 6 where t is and do the arithmetic.

  M(6) = 50(e^(-0.75·6)) = 50e^-4.5 ≈ 0.56

Olivia will have about 0.56 mg of medication remaining in her blood.

Answer:

28.27 cm^2 (2 decimal places)

Step-by-step explanation:

side of box = 24/4 = 6

diameter of coin would be 6 too

area of coin = pi x (6/2)^2 = 28.2743

Answer:

9 boards

Step-by-step explanation:

2/3 of the porch= 6 boards

so to figure out how much one third of the porch needs you find half of what it takes to fill in 2/3 of the porch and you get 3.

so 3=1/3 of the porch

then you simply do 3times 3 or 3+3+3 and you get 9

so it takes 9 boards to fill the whole porch

Final answer:

Four possible solutions to the inequality X > -1 are 0, 1, 2, and 2.5, as each of these values is greater than -1. The solution set in interval notation is (-1, ∞).

Explanation:

The inequality in question is X > -1. To provide four possible solutions, we are essentially looking for any four numbers that are greater than -1. Remember, there are an infinite number of solutions since X can be any value greater than -1, but here are four specific examples:

Each of these values satisfies the inequality X > -1, because they are all greater than -1. It is important to note that solutions to inequalities like this one are often represented in interval notation, in this case, it would be (-1, ∞), meaning any number greater than -1 but less than infinity.

To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we can use the formula n = (Z/E)^2 * p * (1-p).

To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we need to calculate the minimum sample size n required. We can use the formula:

n = (Z₃/E)^2 * p * (1-p)

Where Z₃ is the critical value, E is the maximum error tolerance (which is half the width of the confidence interval), and p is the estimated proportion of adult Americans who support the changes.

For part (a), where 20% of all adult Americans support the changes, the estimated proportion p is 0.20. Plugging in the values for Z₃ and E, we can solve for n. Similarly, for part (b), where 25% of all adult Americans support the changes, the estimated proportion p is 0.25. Plugging in the values for Z₃ and E, we can solve for n.

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(a) The researcher needs to sample 15 more adult Americans if 20% support the changes.

(b) The researcher needs to sample 5 more adult Americans if 25% support the changes.

To determine how many more adult Americans the researcher needs to sample for the distribution of the sample proportion to be approximately normal, we need to use the Central Limit Theorem (CLT).

According to the CLT, the sampling distribution of the sample proportion [tex]\(\hat{p}\)[/tex] is approximately normal if both [tex]\(n \hat{p} \geq 10\)[/tex] and [tex]\(n (1 - \hat{p}) \geq 10\)[/tex], where n is the sample size and [tex]\(\hat{p}\)[/tex] is the sample proportion.

Let's find the required sample size for both cases:

Case (a): 20% of all adult Americans support the changes

Given [tex]\(\hat{p} = 0.20\),[/tex]

To ensure normality:

[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]

1. [tex]\( n \hat{p} \geq 10 \)[/tex]

  [tex]\[ n \times 0.20 \geq 10 \implies n \geq \frac{10}{0.20} = 50 \][/tex]

2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]

  [tex]\[ n \times 0.80 \geq 10 \implies n \geq \frac{10}{0.80} = 12.5 \][/tex]

The stricter condition is [tex]\( n \geq 50 \).[/tex]

Since the researcher already has a sample size of 35, the additional number of adults needed is:

[tex]\[50 - 35 = 15\][/tex]

Case (b): 25% of all adult Americans support the changes

Given [tex]\(\hat{p} = 0.25\),[/tex]

To ensure normality:

[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]

1. [tex]\( n \hat{p} \geq 10 \)[/tex]

  [tex]\[ n \times 0.25 \geq 10 \implies n \geq \frac{10}{0.25} = 40 \][/tex]

2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]

  [tex]\[ n \times 0.75 \geq 10 \implies n \geq \frac{10}{0.75} = 13.33 \][/tex]

The stricter condition is [tex]\( n \geq 40 \).[/tex]

Since the researcher already has a sample size of 35, the additional number of adults needed is:

[tex]\[40 - 35 = 5\][/tex]

Answer:

  0.80

Step-by-step explanation:

The z-score is found from the formula ...

  Z = (X -μ)/σ

  Z = (77 -73)/5 = 4/5 = 0.80

Jennifer's Z-score was 0.80.

Answer:

86.64% probability that the resulting sample proportion is within .02 of the true proportion.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For the sampling distribution of a sample proportion p in a sample of size n, we have that [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem:

[tex]\mu = 0.2, \sigma = \sqrt{\frac{0.2*0.8}{900}} = 0.0133[/tex]

How likely is the resulting sample proportion to be within .02 of the true proportion (i.e., between .18 and .22)?

This is the pvalue of Z when X = 0.22 subtracted by the pvalue of Z when X = 0.18.

X = 0.22

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.22 - 0.2}{0.0133}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332.

X = 0.18

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.18 - 0.2}{0.0133}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that the resulting sample proportion is within .02 of the true proportion.

Final answer:

To calculate the probability that both a seventh grader and an eighth grader selected at random are girls, multiply the probability of selecting a girl from each grade. For the seventh grade, it's 1/4, and for the eighth grade, it's 7/10. The overall probability of both being girls is therefore 7/40.

Explanation:

The question involves determining the probability that both students selected for a competition from different grades are girls. To find this, we need to consider the number of girls in each of the two grades separately.

In the seventh grade, there are 3 girls out of 12 students. So, the probability of selecting a girl from the seventh grade is 3/12, which simplifies to 1/4. In the eighth grade, there are 7 girls out of 10 students. Therefore, the probability of selecting a girl from the eighth grade is 7/10.

To find the overall probability of selecting girls from both grades, we multiply the probabilities of each event since they are independent: (1/4) * (7/10) = 7/40.

Thus, the probability that both selected students are girls is 7/40.